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In a certain year, the difference between Mary's and Jim's

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In a certain year, the difference between Mary's and Jim's  [#permalink]

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In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.

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Originally posted by alimad on 25 Nov 2007, 19:12.
Last edited by Bunuel on 04 Mar 2013, 03:38, edited 1 time in total.
Edited the question and added OA.
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Re: In a certain year, the difference between Mary's and Jim's  [#permalink]

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New post 30 Aug 2016, 06:52
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alimad wrote:
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.


Let's first deal with the given information.
Let J = Jim's salary
Let M = Mary's salary
Let K = Kate's salary

Notice that the salaries (in ascending order) must be J, K, M
Also, if the difference between Mary's and Jim's annual salaries equals twice the difference between Mary's and Kate's annual salaries, then we can conclude that the 3 salaries are equally spaced.

Target question: What was the average annual salary of the 3 people that year?

Statement 1: Jim's annual salary was $30,000 that year.
In other words, J = 30,000
So, the three salaries, arranged in ascending order are: 30,000, K, M
Plus we know that the 3 salaries are equally spaced.
Do we now have enough information to answer the target question? No.

For proof that that we don't have enough information, consider these 2 cases:
Case a: J=30,000, K=30,001, M=30,002, in which case the average salary is $30,001
Case b: J=30,000, K=30,002, M=30,004, in which case the average salary is $30,002
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Kate's annual salary was $40,000 that year.
In other words, K = 40,000
Perfect!
Since the 3 salaries are equally spaced, we can use a nice rule that says, "If the numbers in a set are equally spaced, then the mean and median of that set are equal"
Since Kate's salary must be the median salary, we now know that the average salary must be $40,000
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer =

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Re: Annual Salary _ DS  [#permalink]

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New post 25 Nov 2007, 23:53
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alimad wrote:
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kat's annual salaries. If Mary's annual salry was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

Jim's annual salary was $30,000 that year
Kate's annual salary was $40,000 that year


M + J + K / 3 = ?

Statement I

M - 30,000 = 2(M-K) - Plug in Numbers

50,000 - 30,000 = 2 (50,000 - 40000)
20,000 = 200000

50+30 + 40 = 120/3 = 40,000

60,000 - 30,000 = 2 (60,000 - 45,000)
30,000 = 30,000

60+30 + 45 = 135 /3 = 4..... - insufficient

Statement II

M - J = 2 (M - 40,000)

Plug Numbers
50,000 - 30,000 = 2 (50,000 = 40,000)
50 + 40 + 30 = 120 /3 = 40 average

60,000 - 20,000 = 2( 60,000 - 40,000)
40,000 = 40,000

60 + 20 + 40 = 120/3 = 40 average --- Answer is B

This approach takes a long time. Please provide an alternative solution. Thanks


Woah, slow down there killer. Thats too much work!

equation from stem: M-J=2(M-K) --> M-K=2M-2K --> M=2K-J

We want to know (M+J+K)/3

2K-J+J+K --> 3K/3 --> K is the average. If we know K then Suff.

So B is the answer.

Make sure to double check though to see if we can't get any others similar to 3K/3. ex/ maybe we can get 3J/3 or 4J/3 and so on... turns out we can't.
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New post 25 Nov 2007, 21:13
1
I think answer should be C.

From stem:
M-J = 2(M-K)
M-J = 2M-2K
M = 2K-J

what's M+J+K/3?

1) J = 30
M = 2K-30, insuff.

2) K = 40
M = 80-J, insuff.

1&2)
M = 80-30 = 50, suff.[/code]
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New post 16 Dec 2007, 13:08
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1
im with B.

You can create an equation from stem of m-j=2(m-k), and you are looking for m+j+k/3

If you expand and plug in, you will see that average is just k, i.e. kates salary. B gives you this info
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New post 01 Aug 2008, 21:06
2
ryguy904 wrote:
Data Sufficiency:

In a certain year, the difference between Mary's and Jim's annual salary was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary is the highest of the three people, what was the average (arithmetic mean) annual salary of the 3 people last year?

1) Jim's annual salary was $30,000 that year
2) Kate's annual salary was $40,000 that year.


Clearly IMO B

consider the given condition=>say mary's sal =m,ken's=k,jim's=j
then given that => m-j = 2(m-k) =>m+j=2k
now consider Question :( m+j+k) /3 =? that is
3k/3=k =? hence knowig k is sufficient to answr but knowing j is not suffi.hence (1) is not suffi and (2) is sufficient
hence IMO B
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Re: In a certain year, the difference between Mary's and Jim's  [#permalink]

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New post 01 Mar 2013, 12:50
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Let me try too clarify this one for you.

Let Mary's, Jim's and Kate's salaries be M,J and K respectively.
The question states that

(M-J)=2(M-K). This implies that -J=M-2K ==>M+J=2K
We also know that Mary's salary was the highest among the three people.
We need to find (M+K+J)/3=3K/3=K
Hence, all we need is Kate's Salary.

Now let us consider statement 1. It tells is about Jim's salary. However, we still do not know the difference between Mary's and Jim's salaries or Mary's salary. So, we cannot go further with this calculations.
INSUFFICIENT

Let us consider statement 2.
This gives us exactly what we want, so this is SUFFICIENT.

Hence, answer is B.
Hope this helped!

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How do you solve this one? what's the answer?
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Re: Annual Salary _ DS  [#permalink]

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New post 11 Oct 2013, 04:11
GMATBLACKBELT wrote:
alimad wrote:
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kat's annual salaries. If Mary's annual salry was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

Jim's annual salary was $30,000 that year
Kate's annual salary was $40,000 that year


M + J + K / 3 = ?

Statement I

M - 30,000 = 2(M-K) - Plug in Numbers

50,000 - 30,000 = 2 (50,000 - 40000)
20,000 = 200000

50+30 + 40 = 120/3 = 40,000

60,000 - 30,000 = 2 (60,000 - 45,000)
30,000 = 30,000

60+30 + 45 = 135 /3 = 4..... - insufficient

Statement II

M - J = 2 (M - 40,000)

Plug Numbers
50,000 - 30,000 = 2 (50,000 = 40,000)
50 + 40 + 30 = 120 /3 = 40 average

60,000 - 20,000 = 2( 60,000 - 40,000)
40,000 = 40,000

60 + 20 + 40 = 120/3 = 40 average --- Answer is B

This approach takes a long time. Please provide an alternative solution. Thanks


Woah, slow down there killer. Thats too much work!

equation from stem: M-J=2(M-K) --> M-K=2M-2K --> M=2K-J

We want to know (M+J+K)/3

2K-J+J+K --> 3K/3 --> K is the average. If we know K then Suff.

So B is the answer.

Make sure to double check though to see if we can't get any others similar to 3K/3. ex/ maybe we can get 3J/3 or 4J/3 and so on... turns out we can't.


I think your rationale is good, however just wanted to know something.
When they mention the difference between Mark, Jane, etc. Don't we need to put it in Absolute Value?

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Re: Annual Salary _ DS  [#permalink]

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New post 11 Oct 2013, 04:31
3
jlgdr wrote:
GMATBLACKBELT wrote:
alimad wrote:
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kat's annual salaries. If Mary's annual salry was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

Jim's annual salary was $30,000 that year
Kate's annual salary was $40,000 that year


M + J + K / 3 = ?

Statement I

M - 30,000 = 2(M-K) - Plug in Numbers

50,000 - 30,000 = 2 (50,000 - 40000)
20,000 = 200000

50+30 + 40 = 120/3 = 40,000

60,000 - 30,000 = 2 (60,000 - 45,000)
30,000 = 30,000

60+30 + 45 = 135 /3 = 4..... - insufficient

Statement II

M - J = 2 (M - 40,000)

Plug Numbers
50,000 - 30,000 = 2 (50,000 = 40,000)
50 + 40 + 30 = 120 /3 = 40 average

60,000 - 20,000 = 2( 60,000 - 40,000)
40,000 = 40,000

60 + 20 + 40 = 120/3 = 40 average --- Answer is B

This approach takes a long time. Please provide an alternative solution. Thanks


Woah, slow down there killer. Thats too much work!

equation from stem: M-J=2(M-K) --> M-K=2M-2K --> M=2K-J

We want to know (M+J+K)/3

2K-J+J+K --> 3K/3 --> K is the average. If we know K then Suff.

So B is the answer.

Make sure to double check though to see if we can't get any others similar to 3K/3. ex/ maybe we can get 3J/3 or 4J/3 and so on... turns out we can't.


I think your rationale is good, however just wanted to know something.
When they mention the difference between Mark, Jane, etc. Don't we need to put it in Absolute Value?

Cheers
J


Notice that we are told that "Mary's annual salary was the highest of the 3 people", thus |M-J|=M-J and |M-K|=M-k, so no need of modulus here.
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Re: Annual Salary _ DS  [#permalink]

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New post 20 Nov 2013, 19:32
Bunuel wrote:

Notice that we are told that "Mary's annual salary was the highest of the 3 people", thus |M-J|=M-J and |M-K|=M-k, so no need of modulus here.


Okay, I as wondering how that statement was helpful.
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Re: Annual Salary _ DS  [#permalink]

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New post 16 May 2014, 02:47
2
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We don't need to use algebra for this right?

We know that:
A) the order is Mary --> Kate --> Jim
B) the difference between Mary and Kate is twice the difference between Mary and Jim - this is an arithmetic progression with 3 integers.

For statements:
1) We know Jim's annual salary but not the difference - meaning we do not know Kate or Mary's annual salary. We cannot find the average. (not sufficient)

2) We know Kate's annual salary. For an arithmetic progression of an odd number of integers, the average is the the middle integer. Kate's salary is the average. (sufficient)

What do you think?

Bunuel wrote:
jlgdr wrote:
GMATBLACKBELT wrote:

Woah, slow down there killer. Thats too much work!

equation from stem: M-J=2(M-K) --> M-K=2M-2K --> M=2K-J

We want to know (M+J+K)/3

2K-J+J+K --> 3K/3 --> K is the average. If we know K then Suff.

So B is the answer.

Make sure to double check though to see if we can't get any others similar to 3K/3. ex/ maybe we can get 3J/3 or 4J/3 and so on... turns out we can't.


I think your rationale is good, however just wanted to know something.
When they mention the difference between Mark, Jane, etc. Don't we need to put it in Absolute Value?

Cheers
J


Notice that we are told that "Mary's annual salary was the highest of the 3 people", thus |M-J|=M-J and |M-K|=M-k, so no need of modulus here.
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Re: Annual Salary _ DS  [#permalink]

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New post 16 May 2014, 03:47
1
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ShannonWong wrote:
We don't need to use algebra for this right?

We know that:
A) the order is Mary --> Kate --> Jim
B) the difference between Mary and Kate is twice the difference between Mary and Jim - this is an arithmetic progression with 3 integers.

For statements:
1) We know Jim's annual salary but not the difference - meaning we do not know Kate or Mary's annual salary. We cannot find the average. (not sufficient)

2) We know Kate's annual salary. For an arithmetic progression of an odd number of integers, the average is the the middle integer. Kate's salary is the average. (sufficient)

What do you think?

Bunuel wrote:
Notice that we are told that "Mary's annual salary was the highest of the 3 people", thus |M-J|=M-J and |M-K|=M-k, so no need of modulus here.


Yes, your approach is correct.
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Re: In a certain year, the difference between Mary's and Jim's  [#permalink]

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New post 12 Aug 2014, 02:01
2
My approach was as follows:

Kate = k
Jim = j
Mary = m

From the stem we can create the following equation:
m - j = 2 (m -k)
m - j = 2m - 2k
2k = m + j

What we need to find is:

(m + j + k) / 3

Statement 1 gives us only j, which is clearly insufficient

Statement 2 gives us k = 40. So we can solve our equation:
2k = 80 => m + j = 80

So, (m + j + k) / 3 = (40 + 80) / 3 = 40. Sufficient.
ANSWER B.
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New post 30 Nov 2014, 22:48
I agree of all your opinion.
But how do you think about my approach?

We can think that the ratio of Mary:Kate:Jim is 5a:4a:1a, because the difference of Mary and Jim is twice of that of Mary and Kate.
Then the answer could be 'D'.
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New post 01 Dec 2014, 03:03
AnthonySS wrote:
I agree of all your opinion.
But how do you think about my approach?

We can think that the ratio of Mary:Kate:Jim is 5a:4a:1a, because the difference of Mary and Jim is twice of that of Mary and Kate.
Then the answer could be 'D'.


How do you get this ratio?

m - j = 2 (m -k)
m - j = 2m - 2k
2k = m + j

We cannot get the ratio m:k:j from 2k = m + j.
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Re: In a certain year, the difference between Mary's and Jim's  [#permalink]

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New post 01 Dec 2014, 19:06
Bunuel wrote:
AnthonySS wrote:
I agree of all your opinion.
But how do you think about my approach?

We can think that the ratio of Mary:Kate:Jim is 5a:4a:1a, because the difference of Mary and Jim is twice of that of Mary and Kate.
Then the answer could be 'D'.


How do you get this ratio?

m - j = 2 (m -k)
m - j = 2m - 2k
2k = m + j

We cannot get the ratio m:k:j from 2k = m + j.



---------------------------------------------------------------------

My apologies. I meant that 'M:K:J = 3a:2a:1a', therefore M-J=2a and M-K=a. The difference is twice.
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Re: In a certain year, the difference between Mary's and Jim's  [#permalink]

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New post 01 Dec 2014, 23:37
AnthonySS wrote:
Bunuel wrote:
AnthonySS wrote:
I agree of all your opinion.
But how do you think about my approach?

We can think that the ratio of Mary:Kate:Jim is 5a:4a:1a, because the difference of Mary and Jim is twice of that of Mary and Kate.
Then the answer could be 'D'.


How do you get this ratio?

m - j = 2 (m -k)
m - j = 2m - 2k
2k = m + j

We cannot get the ratio m:k:j from 2k = m + j.



---------------------------------------------------------------------

My apologies. I meant that 'M:K:J = 3a:2a:1a', therefore M-J=2a and M-K=a. The difference is twice.


Again, from 2k = m + j we cannot get the ratio. It's not necessary the ratio to be 3:2:1.
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Re: In a certain year, the difference between Mary's and Jim's  [#permalink]

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New post 15 Feb 2015, 01:56
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With DS problems, I like to start by figuring out as much info as possible from the prompt. So, we know that
M-J=2(M-K) which we can simplify to M=2K-J

(because we know that Mary has the highest salary. We also know that M>K>J because the difference between mary and jim is bigger

We are looking for the average, so if we can figure out the sum (M+J+K), which we can substitute in the new M and get 2K-J+K+J, or 3K
so basically, all we need is J and we know the average.

(I) tells us that J=30,000, which doesn't really help us
(II) gives us K, which is 40,000, so we know the sum is 120,000 and the average is 40,000
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Re: In a certain year, the difference between Mary's and Jim's  [#permalink]

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New post 02 Mar 2015, 02:21
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.

Hi Bunuel,
I am also getting A as suff.

M-J=2(M-K)
Thus,K=2J
Now M-J-2(M-K)
Substitute K=2J
WE GET 3J=M
So M+J+K/3=3J+J+2J/3
2J=This is average,and we are given J,so suff
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Re: In a certain year, the difference between Mary's and Jim's  [#permalink]

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New post 02 Mar 2015, 02:37
ssriva2 wrote:
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7

(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.

Hi Bunuel,
I am also getting A as suff.

M-J=2(M-K)
Thus,K=2J
Now M-J-2(M-K)
Substitute K=2J
WE GET 3J=M
So M+J+K/3=3J+J+2J/3
2J=This is average,and we are given J,so suff


How do you get K=2J from M-J=2(M-K)?
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Re: In a certain year, the difference between Mary's and Jim's &nbs [#permalink] 02 Mar 2015, 02:37

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